I know that given a complex number in form $x + iy$ we have the following:
$$
x=r\cos\theta\\
y=r\sin\theta
$$
And I know that $r=\left|x+iy\right|$.
$$
r=\sqrt{1^2+(-\sqrt3)^2}=\sqrt{4}=2
$$
This all yields,
\begin{align*}
1&=2\cos\theta\\
\frac{1}{2}&=\cos\theta\\
\theta&=\frac{\pi}{3}=\frac{5\pi}{3}\quad\text{(for }\cos\theta\text{)}\\
\\\
-\sqrt3&=2\sin\theta\\
\frac{-\sqrt3}{2}&=\sin\theta\\
\theta&=\frac{-\pi}{3}=\frac{5\pi}{3}\quad\text{(for }\sin\theta\text{)}
\end{align*}
Which gives me a polar form as follows.
$$
1-\sqrt{3}i=2\left(\cos{\frac{5\pi}{3}}+\sin{\frac{5\pi}{3}}\right)
$$